A tangential force acts on the rim of a 2.0 kilogram disk-shaped wheel (0.50 m radius) and gives the wheel an angular acceleration of 4.8 rad/s^2. Neglect friction and find the magnitude of the force.
To find the magnitude of the tangential force acting on the wheel, we can use Newton's second law for rotational motion, which states that the torque applied to an object is equal to the product of its moment of inertia and angular acceleration.
The moment of inertia of a disk-shaped wheel can be calculated using the formula I = 0.5 * m * r^2, where I is the moment of inertia, m is the mass of the wheel, and r is the radius of the wheel.
In this case, the mass of the wheel is given as 2.0 kilograms and the radius is given as 0.50 meters. Plugging these values into the formula, we can calculate the moment of inertia:
I = 0.5 * 2.0 kg * (0.50 m)^2
= 0.5 * 2.0 kg * 0.25 m^2
= 0.5 kg * m^2
Now, we can use the formula for torque (τ) to relate it with the tangential force (F) and the moment of inertia (I):
τ = I * α
Where α is the angular acceleration. Rearranging the formula, we have:
F = τ / r
Since we are given the angular acceleration (α) as 4.8 rad/s^2 and the radius (r) as 0.50 meters, we can substitute these values into the formula to find the torque:
τ = I * α
= (0.5 kg * m^2) * (4.8 rad/s^2)
= 2.4 kg * m^2/s^2
Finally, we can substitute this value into the formula for the force (F) to find the magnitude of the tangential force:
F = τ / r
= (2.4 kg * m^2/s^2) / (0.50 m)
= 4.8 N
Therefore, the magnitude of the tangential force acting on the wheel is 4.8 Newtons.